基于delta方法泊松分布参数的近似信仰推断

Approximate fiducial inference for the parameter of Poisson distribution based on delta method

文章主要研究了Poisson分布参数λ的近似信仰推断,利用对数变换后的估计量的渐近正态性对λ建立近似的枢轴方程,并得到其近似信仰分布和置信区间。模拟结果表明,近似信仰区间与Wald置信区间的平均长度几乎无差异,但近似信仰置信区间覆盖概率明显优于Wald置信区间的覆盖概率。

This paper mainly discusses the approximate fiducial inference of Poisson distribution with the parameter λ. An approximate pivotal equation about ）, is constructed based on the asymptotic normality of a logarithrnie-transformed estimator. Then an approximate fiducial distribution and confidence interval of the Poisson parameter are obtained. The simulation results indicate that the average burst length of the approximate fiducial interval and the Wald confidence interval is almost the same, but the coverage probability of the approximate fiducial interval is obviously superior to the Wald confidence interval＇ s.